Question: Simplify the following expression: $ k = \dfrac{10z - 6}{9} + \dfrac{8}{9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{10z - 6}{9} \times \dfrac{9}{9} = \dfrac{90z - 54}{81} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{8}{9} \times \dfrac{9}{9} = \dfrac{72}{81} $ Therefore $ k = \dfrac{90z - 54}{81} + \dfrac{72}{81} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{90z - 54 + 72}{81} $ $k = \dfrac{90z + 18}{81}$ Simplify the expression by dividing the numerator and denominator by 9: $k = \dfrac{10z + 2}{9}$